MATLAB - 1D Schrodinger wave equation (Time independent system)

% =========================================================================
%                Program to solve 1D infinite well problem
% ***************************** By Mahesha MG *****************************
% This is to solve 1D Schrodinger wave equation (Time independent system)
% by finite difference method -- boundary value problem

% Date: 07/09/2012
% =========================================================================
clc;
clear;
x0=0;
m=1.1;
sum2=1;
n=input('Enter energy state n: ');
xl=input('Enter length of the well(in nm): ');
while(floor(m)<m)
    h=input('Enter stepsize in nm: ');
    m=(xl-x0)/h;
    if floor(m)<m
        warning('Step size is wrong. Enter proper value')
    end

end
x=x0:h:xl;
y=zeros(size(x));
y(1)=0;
y(m+1)=0;
y(2)=1;
for i=3:m
    y(i) = -(y(i-2)+((-2+(n*n*pi*pi*h*h/(xl*xl)))*y(i-1)));
    sum2=sum2+y(i)^2;
end
y=y/sqrt(sum2); %normalization
y2=y.^2;       %y2 gives probability density
figure('color','white')
subplot(2,1,1), plot(x,y,'r')
title('By Mahesha MG')
xlabel('Distance in nm')
ylabel('wave function')
subplot(2,1,2),plot(x,y2)
xlabel('Distance in nm')
ylabel('probability density')

Published with MATLAB® 7.13

Enter energy state n: 10

Enter length of the well(in nm): 10

Enter stepsize in nm: 0.01